The Borel transform and linear nonlocal equations: applications to zeta-nonlocal field models

Chávez, Alan; Prado, Humberto; Reyes, Enríque G.

doi:10.48550/arxiv.1907.02617

Cited by 1 publication

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References 31 publications

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“…Instead of the Riemann zeta function one can try construction of Lagrangians with some similar functions. In [15], embedding of the Dirichlet L-function was proposed.…”

Section: Discussionmentioning

confidence: 99%

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From $p$-Adic to Zeta Strings

Dragovich

2020

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This article is related to construction of zeta strings from p-adic ones. In addition to investigation of p-adic string for a particular prime number p, it is also interesting to study collective effects taking into account all primes p. An idea behind this approach is that a zeta string is a whole thing with infinitely many faces which we see as p-adic strings. The name zeta string has origin in the Riemann zeta function contained in related Lagrangian. The starting point in construction a zeta string is Lagrangian for a p-adic open string. There are two types of approaches to get a Lagrangian for zeta string from Lagrangian for p-adic strings: additive and multiplicative approaches, that are related to two forms of the definition of the Riemann zeta function. As a result of differences in approaches, one obtains several different Lagrangians for zeta strings. We briefly discuss some properties of these Lagrangians, related potentials, equations of motion, mass spectrum and possible connection with ordinary strings. This is a review of published papers with some new views. * This article is based on a talk given at the first Conference on Nonlinearity, held in Belgrade, 11-12 October 2019, and dedicated to the 110th anniversary of Nikolay Nikolayevich Bogolyubov -an outstanding Soviet and Russian scientist.

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“…Instead of the Riemann zeta function one can try construction of Lagrangians with some similar functions. In [15], embedding of the Dirichlet L-function was proposed.…”

Section: Discussionmentioning

confidence: 99%

“…Solution of equation of motion (34) is investigated in [15], where LHS is simplified by an entire function of exponential type. [8,9].…”

Section: Additive Approachmentioning

confidence: 99%

From $p$-Adic to Zeta Strings

Dragovich

2020

Preprint

View full text Add to dashboard Cite

show abstract

The Borel transform and linear nonlocal equations: applications to zeta-nonlocal field models

Cited by 1 publication

References 31 publications

From $p$-Adic to Zeta Strings

From $p$-Adic to Zeta Strings

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